Inequalities for covering codes
- 1 September 1988
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 34 (5) , 1276-1280
- https://doi.org/10.1109/18.21257
Abstract
Any code C with covering radius R must satisfy a set of linear inequalities that involve the Lloyd polynomial L R(x); these generalize the sphere bound. Syndrome graphs associated with a linear code C are introduced to help keep track of low-weight vectors in the same coset of C (if there are too many such vectors C cannot exist). Illustrations show that t[17, 10]=3 and t[23, 15]=3 where t[n, k] is the smallest covering radius of any [n, k] codeKeywords
This publication has 5 references indexed in Scilit:
- The minimal covering radius t(15,6) of a six-dimensional binary linear code of length 15 is equal to 4IEEE Transactions on Information Theory, 1988
- Improved sphere bounds on the covering radius of codesIEEE Transactions on Information Theory, 1988
- An updated table of minimum-distance bounds for binary linear codesIEEE Transactions on Information Theory, 1987
- Covering radius---Survey and recent resultsIEEE Transactions on Information Theory, 1985
- On the covering radius of codesIEEE Transactions on Information Theory, 1985